I'm sorry Stephen but I have to disagree with some of the points in your argument on the profile (I know nothing about this particular family so I'm just giving my opinion from general points) I don't think you can equate Richard baptised in 1588 with the unbaptised child buried in 1590. There is still the possibility that the parents of Richard in Repton are the parents of later children in Stoke.
1) The burial of the unbaptised child clearly took place in May 1590 It appears under the heading of Ann Domini 1590 see (ignore index entry which will appear which is for An, the sister, baptised in November 1591)
2) You are equating this burial with a child baptised as Richard in November 1588 in Repton. To me this doesn't seem right.
This child has no name at burial because he was unbaptised. This was a really important and devastating thing for a vicar to write and occurs very rarely. I doubt that the vicar in May 1590 would contemplate that a child of 18 months would be unbaptised. Names are given during the baptism ceremony and theologically without baptism there was no certainty of redemption. An unbaptised child would normally have been buried outside the consecrated area of the churchyard. There would be no funeral service and indeed there are probably burials of unbaptised infants that go unrecorded. In this period, to avoid this fate baptisms took place on the first Sunday or holy day after birth. Sickly babies who were thought to be at risk of dying were usually baptised immediately after birth by the midwife or the vicar was called in. The fear of unbaptised death meant that sometimes babies were baptised before the child had been fully born and its sex known (Creature was one name used for such baptisms)